Problem: What do the following two equations represent? $2x+5y = 2$ $-5x+2y = -4$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x+5y = 2$ $5y = -2x+2$ $y = -\dfrac{2}{5}x + \dfrac{2}{5}$ Putting the second equation in $y = mx + b$ form gives: $-5x+2y = -4$ $2y = 5x-4$ $y = \dfrac{5}{2}x - 2$ The slopes are negative inverses of each other, so the lines are perpendicular.